FIG. 5 is a circuit diagram representing a schematic configuration of an LLC current resonant converter 1, as an example of a conventional LLC resonant converter.
As shown in FIG. 5, the LLC current resonant converter 1 includes a bridge circuit 10 configured to receive a DC input voltage Vin, an LLC resonant circuit 20 connected to the bridge circuit 10, a transformer 30 connected to the LLC resonant circuit 20, and a rectifier circuit 40 connected to the transformer 30 and configured to send out a converted DC voltage.
The bridge circuit 10 has series-connected switches Q1, Q2. The states of these switches are changed in time sequence with predetermined timing. By such switching operations, the bridge circuit 10 sends out square-wave voltages at a connection point 10a between the switches Q1, Q2 and at a GND 10b. 
The LLC resonant circuit 20 has a resonant capacitor Cr, an end of which is connected to the GND 10b of the bridge circuit 10. The resonant capacitor Cr, as well as a magnetizing inductance Lm and a leakage inductance Lr to be described later, forms the resonant circuit.
The transformer 30 includes a primary winding 31 and a secondary winding 32, which are isolated from each other. The magnetizing inductance Lm is connected in parallel to first and second ends of the primary winding 31. The leakage inductance Lr is connected in series to the first end of the primary winding 31. The first end of the primary winding 31 is connected to the connection point 10a of the switches Q1, Q2, via the leakage inductance Lr. The second end of the primary winding 31 is connected to the GND 10b of the bridge circuit 10, via the resonant capacitor Cr. The secondary winding 32 is provided with a center tap 32m. 
The rectifier circuit 40 includes rectifier elements D1, D2 whose anodes (positive electrodes) are respectively connected to first and second ends of the secondary winding 32, a positive output terminal 42a connected to cathodes (negative electrodes) of the rectifier elements, a negative output terminal 42b connected to the center tap 32m of the secondary winding 32, a current smoothing capacitor 41 connected between the pair of output terminals 42a, 42b so as to smooth the electric current. Through this rectifier circuit, a DC output voltage Vo is generated at the pair of output terminals 42a, 42b. 
This LLC current resonant converter 1 is an isolated DC/DC converter that can reduce a switching loss and noise that occur in the semiconductor devices on the primary side and the secondary side, by utilizing resonance of the single capacitance Cr and the two inductances Lm, Lr. Utilization of the leakage inductance Lr and the magnetizing inductance Lm of the transformer 30 reduces the number of elements required in the circuit configuration.
FIG. 6 is a graph showing an example of frequency-gain characteristics of the LLC current resonant converter 1.
The LLC current resonant converter 1 converts an input voltage Vin to a desired output voltage Vo by PFM (pulse frequency modulation) at the switches Q1, Q2. The LLC current resonant converter 1 can control the gain (i.e., a conversion ratio of the output voltage Vo to the input voltage Vin) by changing the frequency in the PFM, and can thus obtain the desired output voltage Vo even when the input voltage Vin has changed. In the LLC current resonant converter 1 shown in FIG. 5, the output voltage and the input voltage have the following relationship:output voltage Vo=(input voltage Vin×gain)/turns ratio N of the transformerwhere N is not necessarily an integer, and N may be 1 or greater, or less than 1. In FIG. 6, fsr represents the resonance frequency when the gain is 1, and fpr represents the resonance frequency when the gain is maximum, Gainmax.
As the range from Gainmax to Gain 1 is greater (the gain is higher), the LLC resonant converter can produce a desired output voltage Vo with a lower input voltage Vin.
FIG. 7 is a schematic view showing a configuration example of a source circuit containing the LLC resonant converter.
In the source circuit 3 shown in FIG. 7, an alternating-current commercial power CP is applied to an PFC (Power Factor Correction: power factor improvement circuit) 2. An isolated DC/DC converter 1A receives an output from the PFC 2, and produces a DC output voltage Vo. A block capacitor Cin connects two connecting lines between the PFC 2 and the isolated DC/DC converter 1A. The LLC current resonant converter 1 according to the present invention can serve as the isolated DC/DC converter 1A.
If power supply from the commercial power CP stops, the source circuit 3 should maintain the output voltage without any loss for a predetermined time (e.g., 20 ms, hereinafter called “retention time t”). During this time, power is supplied by the block capacitor Cin. The minimum capacitance Cinmin of the block capacitor Cin is obtained by the following formula.
                              C          inmin                =                                            2              ⁢              P                                                      V                                  c                  ⁢                                                                          ⁢                  _                  ⁢                                                                          ⁢                  start                                2                            -                              V                                  in                  ⁢                                                                          ⁢                  _                  ⁢                                                                          ⁢                  min                                2                                              ×          t                                    [                  Math          .                                          ⁢          1                ]            
In this formula, P, Vc_start, and Vin_min are defined as below.                P: maximum output power of the isolated DC/DC converter        Vc_start: charging voltage in Cin at the moment when power supply stops        Vin_min: minimum input voltage at which the isolated DC/DC converter is operable        
As understood from this formula, the lower the minimum input voltage Vin_min, the smaller the minimum capacitance Cinmin. The minimum input voltage Vin_min can be reduced as the isolated DC/DC converter 1A has a higher gain. Hence, a high gain enables downsizing of the block capacitor Cin, while keeping the retention time t.
FIG. 8(a) shows an equivalent circuit 1B in the LLC resonant converter including an output load resistance as a load, seen from the primary side of the transformer 30. ZL indicates a parallel connection part in FIG. 8(a). FIG. 8(b) shows an equivalent circuit 1C in which a ZL inductance and a resistance are connected in series. In these circuits, Vsq represents an output voltage of the bridge circuit 10 as a square voltage source, and Req is obtained by the following formula in which the output load resistance on the secondary side of the transformer is converted to the AC resistance on the primary side.
In FIG. 8(b), ZL(Re) and ZL(Im) represent the real part and the imaginary part of ZL, respectively.
                              R          eq                =                                            8              ⁢                              N                2                            ⁢                              R                o                                                    π              2                                =                                    8              ⁢                              L                m                2                            ⁢                              N                2                            ⁢                              R                o                                                                                      π                  2                                ⁡                                  (                                                            L                      m                                        +                                          L                      r                                                        )                                            2                                                          [                  Math          .                                          ⁢          2                ]            
In this formula, Ro represents an output load resistance, and N represents an actual turns ratio (primary:secondary) of the transformer.
The resonance frequency fsr is obtained by the following formula.
                              f          sr                =                  1                      2            ⁢            π            ⁢                                                            L                  r                                ⁢                                  C                  r                                                                                        [                  Math          .                                          ⁢          3                ]            
The resonance frequency fpr is obtained by following formula, based on the equivalent circuit 1C of FIG. 8(b).
                                          f            pr                    =                                    1                              2                ⁢                π                ⁢                                                                            (                                                                        L                          r                                                +                                                                              Z                            L                                                    ⁡                                                      (                            Im                            )                                                                                              )                                        ⁢                                          C                      r                                                                                            =                          1                              2                ⁢                π                ⁢                                                                            (                                                                        L                          r                                                +                                                                                                            L                              m                                                        ⁢                                                          R                              eq                              2                                                                                                                                          R                              eq                              2                                                        +                                                                                          ω                                2                                                            ⁢                                                              L                                m                                2                                                                                                                                                        )                                        ⁢                                          C                      r                                                                                                          ,                                  ⁢                                  ⁢                  ω          =                      2            ⁢            π            ⁢                                                  ⁢                          f              pr                                                          [                  Math          .                                          ⁢          4                ]            
FIG. 9 is a graph showing an example of frequency-gain characteristics and two operating regions of the LLC resonant converter.
As shown in FIG. 9, the operation of the LLC resonant converter is divided into two operating regions at its resonance frequency fpr: a capacitive region (left) and an inductive region (right). In these regions, the LLC resonant converter operates with following features.
<Capacitive Region>                Hard switching (greater switching loss)        The higher the target gain, the higher the frequency.        A shoot-through current flows through the bridge circuit.        
<Inductive Region>                Soft switching (less switching loss)        The higher the target gain, the lower the frequency.        No shoot-through current flows through the bridge circuit.        
Namely, operation of the LLC resonant converter in the inductive region can reduce the switching loss in the high-frequency operation, and eventually the high-frequency operation enables downsizing of the transformer. For this advantage, the LLC resonant converter is usually controlled in the inductive region.
FIG. 10 is a graph showing an example of frequency-gain characteristics of the LLC resonant converter, with different resonant capacitors Cr. FIG. 11 is a graph showing an example of frequency-gain characteristics of the LLC resonant converter, with different magnetizing inductances Lm.
The magnetizing inductance Lm and the resonant capacitor Cr are designable parameters. A high gain is achieved either by a small Lm or a large Cr.
However, as indicated in FIG. 10 and FIG. 11, a small Lm allows conduction of a high current and results in a greater loss (deteriorates efficiency), and a large Cr lowers the operating frequency and obstructs downsizing of the transformer. On the other hand, a large Lm or a small Cr cannot realize a high gain. Thus, a high gain conflicts with a high-frequency and a high efficiency.
In a conventionally proposed manner for achieving a high gain and a high efficiency, an LLC resonant converter can change the capacitance of its resonant capacitor by turning on and off the switch Q3 in accordance with the input voltage Vin (see, for example, PTL 1).
FIG. 12 is a circuit diagram showing a schematic configuration of an LLC resonant converter 1D that can change the capacitance of its resonant capacitor, similar to the LLC resonant converter disclosed in PTL 1. FIG. 13 is a graph showing an example of frequency-gain characteristics of the LLC resonant converter 1D.
The LLC resonant converter 1D is distinguished from the LLC current resonant converter 1 shown in FIG. 5 by a resonant capacitor changeover circuit 50 in which the switch Q3 and a capacitor Crsw are connected in series. The resonant capacitor changeover circuit 50 is connected in parallel to the resonant capacitor Cr in the LLC resonant circuit 20.
In the steady state, as shown in FIG. 12, the switch Q3 is turned off, and the capacitor Crsw is disconnected from the LLC resonant circuit 20. The LLC resonant converter 1D operates with high-frequency characteristics, with the capacitance of the resonant capacitor Cr (“Q3 off time” in FIG. 13).
In contrast, when an input voltage Vin drops, the switch Q3 is turned on. The LLC resonant converter 1D operates with low-frequency characteristics, with the capacitances of the resonant capacitor Cr and the capacitor Crsw (“Q3 on time” in FIG. 13), thereby giving a high gain.
Later, when the input voltage Vin rises again, the switch Q3 is turned off, and the capacitor Crsw is disconnected from the LLC resonant circuit 20 again. The LLC resonant converter 1D operates, as before, with high-frequency characteristics, with the capacitance of the resonant capacitor Cr (“Q3 off time” in FIG. 13).
The LLC resonant converter 1D shown in FIG. 12, operating as described above, can be designed with a large magnetizing inductance Lm, so that a high-frequency, high-efficiency operation can be compatible with a high gain. For such compatibility, however, transition from the operation with low-frequency characteristics to the operation with high-frequency characteristics needs to be controlled properly.
FIG. 14 is a graph for schematically describing an example of control in the LLC resonant converter 1D, during the transition from low-frequency characteristics to high-frequency characteristics.
The LLC resonant converter disclosed in PTL 1, whose circuit configuration is similar to the one shown in FIG. 12, variably controls its power peak by turning on and off a switch M1 (corresponding to Q3 in FIG. 12).
The LLC resonant converter which controls the transition from low-frequency characteristics to high-frequency characteristics by reducing the capacitance of the resonant capacitor is configured “to turn off the changeover switch when the input voltage reaches a changeover voltage or when the operating frequency reaches the resonance frequency fpr”. At the resonance frequency fpr, the gain reaches its peak with high-frequency characteristics. The resonance frequency fpr changes with a load.
However, this method causes two problems due to the transition from low-frequency characteristics to high-frequency characteristics.
Problem 1) The switches Q1, Q2 forming the bridge circuit are broken by a shoot-through current or a surge voltage.
Problem 2) The output voltage Vo is uncontrollable unless the control in the capacitive region is effective.
Problem 1) occurs when the LLC resonant converter operates in the capacitive region. Problem 2) occurs when the LLC resonant converter is controlled in a common manner in the inductive region.
Problem 2) is described more specifically. When the changeover switch is turned off (from Point 1 to Point 2 in FIG. 14) and the operating frequency remains unchanged, the operation with high-frequency characteristics gives a lower gain. Hence, the output voltage Vo, obtained by multiplying the input voltage Vin with the gain, falls to and below the desired voltage. Under normal control, which targets the inductive region, the operating frequency is lowered to obtain the desired output voltage Vo (from Point 2 to Point 3 in FIG. 14). Such control reduces the gain further, and makes the output voltage Vo even lower.